WRRCTR No.92 Numerical Analysis of One-Dimensional Water Infiltration

Abstract

In attempting to numerically solve the nonlinear moisture flow equation, the Galerkin process, which bears a great similarity to direct methods of the calculus of variations, and the Continuous System Modeling Program (CSMP) approach have been employed. In the finite element formulation of the governing equation, systems of nonlinear algebraic equations were developed on the basis of linear two-dimensional triangular elements. These nonlinear algebraic equations were solved simultaneously, at each time step, by a programmed logic of iterations. In the CSMP approach, Boltzmann's function application and layered soils formulation were demonstrated in obtaining horizontal and vertical moisture profiles. The second and third degrees of polynomial interpretations of moisture diffusivity, D(Ө), and hydraulic conductivity, K(Ө), of the media were conducted. However, it was established that the former representation had only very limited applicability (as far as some Hawaiian soils are concerned), because a second degree polynomial can accurately describe the D(Ө) and K(Ө) vs. moisture content, Ө, curves. The finite element, CSMP, and finite difference solutions were investigated and compared for Wahiawa soils with lateral moisture movement. Vertical moisture profiles for the Molokai soils and Tantalus silty clay loams were also investigated by means of the finite element and the CSMP approach, respectively.